Get updates on Eligibility, Admission, Placements Fees Structure
Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Course Overview
The Functional Analysis certification course is a postgraduate level programme in the field of mathematics. The online course mainly focuses on learning partial differential equations with a modern perspective in addition to other topics. The course covers all the fundamental and important theorems, normed linear spaces, and weak topology, etc. The course would be perfect for those candidates who are pre equipped with the information of basic linear algebra and topology. The course deals with 12 different topics that are covered every week.
Candidates who would want to pursue this Functional Analysis online course will get to collect information on linear transformations, different theorems, reflexivity, some practical examples, etc. Candidates would be offered a certificate at the end of the course if they choose to pay for the exam fees and qualify for the exam with passing grades. Candidates can take up this course at any time and there is no rush to complete the Functional Analysis certification syllabus since it is a self-paced online course. The course is provided by IIT, Madras and mentored by the faculty member of the Institute of Mathematical Sciences, Chennai.
Programme Offerings
- video
- Modules
- exam
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 1000 | yes | IMSc Chennai |
- The quoted amount mentioned on the website needs to be paid as the Functional Analysis fees.
- Candidates have the option of not making any payment and still access the Functional Analysis certification course.
Functional Analysis Fees details
Heads | Amount in Rupees |
Exam fees | Rs.1,000 |
Eligibility Criteria
Education
- Candidates who have graduated in Mathematics from a science background.
- Candidates who have knowledge of topology, linear algebra, and measure theory.
Certification Qualifying Details
Applicants who want to register themselves for a certificate need to perform in the offline exam keeping in mind the following criteria-
Candidates need to achieve an average assignment score and exam score and the sum of both should be at least 40 out of 100 marks.
What you will learn
The following information can be obtained through the completion of this course-
- Candidates will learn about normed linear spaces, linear transformations with examples in the Functional Analysis certification.
- Students will learn about Hahn Banach theorems and vector-valued integration in the subject.
- Candidates will get an understanding of Bessel’s inequality, and orthonormal bases in the Functional Analysis training.
- Participants will learn about separable spaces and convex spaces through the training.
- Candidates will learn about compact operators in the course.
- Participants will learn about abstract Fourier services and applications to the calculus of variations.
- Learners will get an understanding of Parseval identity through the Functional Analysis programme.
Who it is for
Following are the students who are apt for this course-
- Candidates who have knowledge of topology, linear algebra, and real analysis, and measure theory.
Admission Details
Entrants should know the provided steps to be able to complete the admission process for the programme-
Step 1- Applicants must visit the given official link - https://onlinecourses.nptel.ac.in/noc21_ma25/preview
Note- Since the join course tab is not available on the website at the current moment, students are requested to wait.
The Syllabus
- Normed linear spaces
- Examples
- Continuous linear transformations
- Examples
- Continuous linear transformations
- Hahn-Banach theorem-extension form
- Reflexivity
- Hahn-Banach theorem-geometric form
- Vector-valued integration
- Baire’s theorem
- The principle of uniform boundedness
- Application to Fourier series
- Open mapping and closed graph theorems
- Annihilators
- Complemented subspaces
- Unbounded operators
- Adjoints
- Weak topology
- Weak topology
- Banach-Alaoglu theorem
- Reflexive spaces
- Separable spaces
- Uniformly convex spaces
- Applications to calculus of variations
- L^p spaces
- Duality
- Riesz representation theorem
- L^p spaces on Euclidean domains
- Convolutions
- Riesz representation theorem
- Hilbert spaces
- Duality
- Riesz representation theorem
- Application to the calculus of variations
- Lax-Milgram lemma
- Orthonormal sets
- Bessel’s inequality
- Orthonormal bases
- Parseval identity
- Abstract Fourier series
- A spectrum of an operator
- Compact operators
- Riesz Fredholm theory
- Spectrum of a compact operator
- The spectrum of a compact self-adjoint operator